The inception of the Relational Graph Convolutional Network (R-GCN) marked a milestone in the Semantic Web domain as a widely cited method that generalises end-to-end hierarchical representation learning to Knowledge Graphs (KGs). R-GCNs generate representations for nodes of interest by repeatedly aggregating parameterised, relation-specific transformations of their neighbours. However, in this paper, we argue that the the R-GCN's main contribution lies in this "message passing" paradigm, rather than the learned weights. To this end, we introduce the "Random Relational Graph Convolutional Network" (RR-GCN), which leaves all parameters untrained and thus constructs node embeddings by aggregating randomly transformed random representations from neighbours, i.e., with no learned parameters. We empirically show that RR-GCNs can compete with fully trained R-GCNs in both node classification and link prediction settings.
Chongqing University（重庆大学）；The University of Queensland（昆士兰大学）
Graph Convolutional Networks (GCNs) achieve great success in non-Euclidean structure data processing recently. In existing studies, deeper layers are used in CCNs to extract deeper features of Euclidean structure data. However, for non-Euclidean structure data, too deep GCNs will confront with problems like "neighbor explosion" and "over-smoothing", it also cannot be applied to large datasets. To address these problems, we propose a model called PathSAGE, which can learn high-order topological information and improve the model's performance by expanding the receptive field. The model randomly …
Graph convolution operator of the GCN model is originally motivated from a localized first-order approximation of spectral graph convolutions. This work stands on a different view; establishing a \textit{mathematical connection between graph convolution and graph-regularized PCA} (GPCA). Based on this connection, GCN architecture, shaped by stacking graph convolution layers, shares a close relationship with stacking GPCA. We empirically demonstrate that the \textit{unsupervised} embeddings by GPCA paired with a 1- or 2-layer MLP achieves similar or even better performance than GCN on semi-supe…
University of Sheffield（谢菲尔德大学）；University of Nottingham（诺丁汉大学）
Graph convolutional network (GCN) is an emerging neural network approach. It learns new representation of a node by aggregating feature vectors of all neighbors in the aggregation process without considering whether the neighbors or features are useful or not. Recent methods have improved solutions by sampling a fixed size set of neighbors, or assigning different weights to different neighbors in the aggregation process, but features within a feature vector are still treated equally in the aggregation process. In this paper, we introduce a new convolution operation on regular size feature maps…
University of Montenegro（黑山大学）；Imperial College London（伦敦帝国理工学院）
Graph Convolutional Neural Networks (GCNN) are becoming a preferred model for data processing on irregular domains, yet their analysis and principles of operation are rarely examined due to the black box nature of NNs. To this end, we revisit the operation of GCNNs and show that their convolution layers effectively perform matched filtering of input data with the chosen patterns (features). This allows us to provide a unifying account of GCNNs through a matched filter perspective, whereby the nonlinear ReLU and max-pooling layers are also discussed within the matched filtering framework. This …
Zhejiang Normal University（浙江师范大学）；School of AI, Bangalore（班加罗尔人工智能学院）；Guizhou University（贵州大学）；Western University（西安大略大学）
Graph Convolutional Networks (GCNs) are widely used in many applications yet still need large amounts of labelled data for training. Besides, the adjacency matrix of GCNs is stable, which makes the data processing strategy cannot efficiently adjust the quantity of training data from the built graph structures.To further improve the performance and the self-learning ability of GCNs,in this paper, we propose an efficient self-supervised learning strategy of GCNs,named randomly removed links with a fixed step at one region (RRLFSOR).RRLFSOR can be regarded as a new data augmenter to improve over-…
Graph Convolutional Networks (GCNs), which use a message-passing paradigm with stacked convolution layers, are foundational methods for learning graph representations. Recent GCN models use various residual connection techniques to alleviate the model degradation problem such as over-smoothing and gradient vanishing. Existing residual connection techniques, however, fail to make extensive use of underlying graph structure as in the graph spectral domain, which is critical for obtaining satisfactory results on heterophilic graphs. In this paper, we introduce ClenshawGCN, a GNN model that employ…
RGE-GCN: Recursive Gene Elimination with Graph Convolutional Networks for RNA-seq based Early Cancer Detection
Department of Computer Science, New Jersey Institute of Technology（计算机科学系，新泽西理工学院）；Department of Data Science, New Jersey Institute of Technology（数据科学系，新泽西理工学院）；Department of Biostatistics（生物统计学系）；Division of Cardiology, Brown University Health（心脏病学部，布朗大学健康中心）；Department of Medicine, Warren Alpert Medical School of Brown University（医学系，布朗大学沃伦·阿尔珀特医学院）
Graph Convolutional Networks (GCNs) have been proved successful in the field of semi-supervised node classification by extracting structural information from graph data. However, the random selection of labeled nodes used by GCNs may lead to unstable generalization performance of GCNs. In this paper, we propose an efficient method for the deterministic selection of labeled nodes: the Determinate Node Selection (DNS) algorithm. The DNS algorithm identifies two categories of representative nodes in the graph: typical nodes and divergent nodes. These labeled nodes are selected by exploring the st…
Xidian University（西安电子科技大学）；University of Montenegro（黑山大学）
Graph convolutional neural network (GCN) has drawn increasing attention and attained good performance in various computer vision tasks, however, there lacks a clear interpretation of GCN's inner mechanism. For standard convolutional neural networks (CNNs), class activation mapping (CAM) methods are commonly used to visualize the connection between CNN's decision and image region by generating a heatmap. Nonetheless, such heatmap usually exhibits semantic-chaos when these CAMs are applied to GCN directly. In this paper, we proposed a novel visualization method particularly applicable to GCN, Ve…
Graph Neural Networks (GNNs) have attracted increasing attention due to its successful applications on various graph-structure data. However, recent studies have shown that adversarial attacks are threatening the functionality of GNNs. Although numerous works have been proposed to defend adversarial attacks from various perspectives, most of them can be robust against the attacks only on specific scenarios. To address this shortage of robust generalization, we propose to defend the adversarial attacks on GNN through applying the Spatio-Temporal sparsification (called ST-Sparse) on the GNN hidd…
Graph convolutional networks (GCNs) are a powerful architecture for representation learning on documents that naturally occur as graphs, e.g., citation or social networks. However, sensitive personal information, such as documents with people's profiles or relationships as edges, are prone to privacy leaks, as the trained model might reveal the original input. Although differential privacy (DP) offers a well-founded privacy-preserving framework, GCNs pose theoretical and practical challenges due to their training specifics. We address these challenges by adapting differentially-private gradien…
Rice University（莱斯大学）；University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；Pacific Northwest National Laboratory（太平洋西北国家实验室）
Graph Convolutional Networks (GCNs) have emerged as the state-of-the-art method for graph-based learning tasks. However, training GCNs at scale is still challenging, hindering both the exploration of more sophisticated GCN architectures and their applications to real-world large graphs. While it might be natural to consider graph partition and distributed training for tackling this challenge, this direction has only been slightly scratched the surface in the previous works due to the limitations of existing designs. In this work, we first analyze why distributed GCN training is ineffective and…
KTH Royal Institute of Technology（瑞典皇家理工学院）；Hive Streaming AB（Hive Streaming AB公司）；Maastricht University（马斯特里赫特大学）
Live video streaming has become a mainstay as a standard communication solution for several enterprises worldwide. To efficiently stream high-quality live video content to a large amount of offices, companies employ distributed video streaming solutions which rely on prior knowledge of the underlying evolving enterprise network. However, such networks are highly complex and dynamic. Hence, to optimally coordinate the live video distribution, the available network capacity between viewers has to be accurately predicted. In this paper we propose a graph representation learning technique on weigh…
Google Research（谷歌研究院）；Columbia University（哥伦比亚大学）
Graph Convolutional Networks (GCNs) have shown significant improvements in semi-supervised learning on graph-structured data. Concurrently, unsupervised learning of graph embeddings has benefited from the information contained in random walks. In this paper, we propose a model: Network of GCNs (N-GCN), which marries these two lines of work. At its core, N-GCN trains multiple instances of GCNs over node pairs discovered at different distances in random walks, and learns a combination of the instance outputs which optimizes the classification objective. Our experiments show that our proposed N-G…
Collaborative filtering (CF) is a long-standing problem of recommender systems. Many novel methods have been proposed, ranging from classical matrix factorization to recent graph convolutional network-based approaches. After recent fierce debates, researchers started to focus on linear graph convolutional networks (GCNs) with a layer combination, which show state-of-the-art accuracy in many datasets. In this work, we extend them based on neural ordinary differential equations (NODEs), because the linear GCN concept can be interpreted as a differential equation, and present the method of Learna…
The Australian Artificial Intelligence Institute (AAII), University of Technology Sydney（悉尼科技大学澳大利亚人工智能研究所（AAII））；Australian Catholic University（澳大利亚天主教大学）
Graph Convolutional Neural Networks (GCNs) has been generally accepted to be an effective tool for node representations learning. An interesting way to understand GCNs is to think of them as a message passing mechanism where each node updates its representation by accepting information from its neighbours (also known as positive samples). However, beyond these neighbouring nodes, graphs have a large, dark, all-but forgotten world in which we find the non-neighbouring nodes (negative samples). In this paper, we show that this great dark world holds a substantial amount of information that might…
Huawei（华为）；École Polytechnique（巴黎综合理工学院）；Institute Polytechnique de Paris（巴黎理工学院）；AUEB（雅典经济与商业大学）
The robustness of the much-used Graph Convolutional Networks (GCNs) to perturbations of their input is becoming a topic of increasing importance. In this paper, the random GCN is introduced for which a random matrix theory analysis is possible. This analysis suggests that if the graph is sufficiently perturbed, or in the extreme case random, then the GCN fails to benefit from the node features. It is furthermore observed that enhancing the message passing step in GCNs by adding the node feature kernel to the adjacency matrix of the graph structure solves this problem. An empirical study of a G…
University of Illinois, Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）
Oversmoothing has been assumed to be the major cause of performance drop in deep graph convolutional networks (GCNs). In this paper, we propose a new view that deep GCNs can actually learn to anti-oversmooth during training. This work interprets a standard GCN architecture as layerwise integration of a Multi-layer Perceptron (MLP) and graph regularization. We analyze and conclude that before training, the final representation of a deep GCN does over-smooth, however, it learns anti-oversmoothing during training. Based on the conclusion, the paper further designs a cheap but effective trick to i…
Enhancing Graph Representations with Neighborhood-Contextualized Message-Passing
Nara Institute of Science and Technology（奈良先端科学技术大学院大学）；Kyoto University（京都大学）；Ateneo de Manila University（马尼拉雅典耀大学）；UNI-President Information Philippines Corporation（统一信息菲律宾公司）；The Chinese University of Hong Kong（香港中文大学）
CNRS（法国国家科学研究中心）；GIPSA-lab（格勒诺布尔交互物理与声学实验室）；NYU Center for Data Science（纽约大学数据科学中心）；IMB（勃艮第数学研究所）；Inria Paris（法国国家信息与自动化研究所巴黎分院）
We study properties of Graph Convolutional Networks (GCNs) by analyzing their behavior on standard models of random graphs, where nodes are represented by random latent variables and edges are drawn according to a similarity kernel. This allows us to overcome the difficulties of dealing with discrete notions such as isomorphisms on very large graphs, by considering instead more natural geometric aspects. We first study the convergence of GCNs to their continuous counterpart as the number of nodes grows. Our results are fully non-asymptotic and are valid for relatively sparse graphs with an ave…
University at Albany, SUNY（纽约州立大学奥尔巴尼分校）；University of Michigan（密歇根大学）
Graph convolutional networks (GCNs) are a widely used method for graph representation learning. We investigate the power of GCNs, as a function of their number of layers, to distinguish between different random graph models on the basis of the embeddings of their sample graphs. In particular, the graph models that we consider arise from graphons, which are the most general possible parameterizations of infinite exchangeable graph models and which are the central objects of study in the theory of dense graph limits. We exhibit an infinite class of graphons that are well-separated in terms of cu…
University of Pennsylvania（宾夕法尼亚大学）；Delft University of Technology（代尔夫特理工大学）
Graph convolutional neural networks (GCNNs) are nonlinear processing tools to learn representations from network data. A key property of GCNNs is their stability to graph perturbations. Current analysis considers deterministic perturbations but fails to provide relevant insights when topological changes are random. This paper investigates the stability of GCNNs to stochastic graph perturbations induced by link losses. In particular, it proves the expected output difference between the GCNN over random perturbed graphs and the GCNN over the nominal graph is upper bounded by a factor that is lin…
The graph convolution network (GCN) is a widely-used facility to realize graph-based semi-supervised learning, which usually integrates node features and graph topologic information to build learning models. However, as for multi-label learning tasks, the supervision part of GCN simply minimizes the cross-entropy loss between the last layer outputs and the ground-truth label distribution, which tends to lose some useful information such as label correlations, so that prevents from obtaining high performance. In this paper, we pro-pose a novel GCN-based semi-supervised learning approach for mul…
Microsoft Research India（微软印度研究院）；IIT Kanpur（印度理工学院坎普尔分校）
Training multi-layer Graph Convolution Networks (GCN) using standard SGD techniques scales poorly as each descent step ends up updating node embeddings for a large portion of the graph. Recent attempts to remedy this sub-sample the graph that reduces compute but introduce additional variance and may offer suboptimal performance. This paper develops the IGLU method that caches intermediate computations at various GCN layers thus enabling lazy updates that significantly reduce the compute cost of descent. IGLU introduces bounded bias into the gradients but nevertheless converges to a first-order…
Univ. of Minnesota（明尼苏达大学）；Digital Tech. Center（数字技术中心）
Graph convolutional networks (GCNs) are vulnerable to perturbations of the graph structure that are either random, or, adversarially designed. The perturbed links modify the graph neighborhoods, which critically affects the performance of GCNs in semi-supervised learning (SSL) tasks. Aiming at robustifying GCNs conditioned on the perturbed graph, the present paper generates multiple auxiliary graphs, each having its binary 0-1 edge weights flip values with probabilities designed to enhance robustness. The resultant edge-dithered auxiliary graphs are leveraged by an adaptive (A)GCN that perform…
Beijing National Research Center for Information Science and Technology (BNRist)（北京信息科学与技术国家研究中心）；Tsinghua University（清华大学）；Tencent AI Lab（腾讯人工智能实验室）
Increasing the depth of GCN, which is expected to permit more expressivity, is shown to incur performance detriment especially on node classification. The main cause of this lies in over-smoothing. The over-smoothing issue drives the output of GCN towards a space that contains limited distinguished information among nodes, leading to poor expressivity. Several works on refining the architecture of deep GCN have been proposed, but it is still unknown in theory whether or not these refinements are able to relieve over-smoothing. In this paper, we first theoretically analyze how general GCNs act …
Elliptic；The University of Sheffield（谢菲尔德大学）；Telecom SudParis（南巴黎电信学院）；Polytechnic Institute of Paris（巴黎综合理工学院）
We show that a modification of the first layer of a Graph Convolutional Network (GCN) can be used to effectively propagate label information across neighbor nodes, for binary and multi-class classification problems. This is done by selectively eliminating self-loops for the label features during the training phase of a GCN. The GCN architecture is otherwise unchanged, without any extra hyper-parameters, and can be used in both a transductive and inductive setting. We show through several experiments that, depending on how many labels are available during the inference phase, this strategy can …
Graph convolutional neural networks (GCNN) have been successfully applied to many different graph based learning tasks including node and graph classification, matrix completion, and learning of node embeddings. Despite their impressive performance, the techniques have a limited capability to incorporate the uncertainty in the underlined graph structure. In order to address this issue, a Bayesian GCNN (BGCN) framework was recently proposed. In this framework, the observed graph is considered to be a random realization from a parametric random graph model and the joint Bayesian inference of the…
Indian Institute of Science（印度科学研究所）；Conduent Labs（康维恩实验室）
Semi-supervised learning on graph structured data has received significant attention with the recent introduction of Graph Convolution Networks (GCN). While traditional methods have focused on optimizing a loss augmented with Laplacian regularization framework, GCNs perform an implicit Laplacian type regularization to capture local graph structure. In this work, we propose Lovasz Convolutional Network (LCNs) which are capable of incorporating global graph properties. LCNs achieve this by utilizing Lovasz's orthonormal embeddings of the nodes. We analyse local and global properties of graphs an…
Indiana University-Purdue University Indianapolis（印第安纳大学-普渡大学印第安纳波利斯分校）
Online social networks (OSNs) classify users into different categories based on their online activities and interests, a task which is referred as a node classification task. Such a task can be solved effectively using Graph Convolutional Networks (GCNs). However, a small number of users, so-called perturbators, may perform random activities on an OSN, which significantly deteriorate the performance of a GCN-based node classification task. Existing works in this direction defend GCNs either by adversarial training or by identifying the attacker nodes followed by their removal. However, both of…
Graph Convolutional Network (GCN) has achieved great success and has been applied in various fields including recommender systems. However, GCN still suffers from many issues such as training difficulties, over-smoothing, vulnerable to adversarial attacks, etc. Distinct from current GCN-based methods which simply employ GCN for recommendation, in this paper we are committed to build a robust GCN model for collaborative filtering. Firstly, we argue that recursively incorporating messages from different order neighborhood mixes distinct node messages indistinguishably, which increases the traini…
National University of Singapore（新加坡国立大学）；PayPal Innovation Lab（PayPal创新实验室）；Alibaba Group（阿里巴巴集团）
A Graph Convolutional Network (GCN) stacks several layers and in each layer performs a PROPagation operation (PROP) and a TRANsformation operation (TRAN) for learning node representations over graph-structured data. Though powerful, GCNs tend to suffer performance drop when the model gets deep. Previous works focus on PROPs to study and mitigate this issue, but the role of TRANs is barely investigated. In this work, we study performance degradation of GCNs by experimentally examining how stacking only TRANs or PROPs works. We find that TRANs contribute significantly, or even more than PROPs, t…
University at Albany, SUNY（纽约州立大学奥尔巴尼分校）；University of Michigan（密歇根大学）
Graph convolutional networks (GCNs) are a widely used method for graph representation learning. To elucidate the capabilities and limitations of GCNs, we investigate their power, as a function of their number of layers, to distinguish between different random graph models (corresponding to different class-conditional distributions in a classification problem) on the basis of the embeddings of their sample graphs. In particular, the graph models that we consider arise from graphons, which are the most general possible parameterizations of infinite exchangeable graph models and which are the cen…
Recently, techniques for applying convolutional neural networks to graph-structured data have emerged. Graph convolutional neural networks (GCNNs) have been used to address node and graph classification and matrix completion. Although the performance has been impressive, the current implementations have limited capability to incorporate uncertainty in the graph structure. Almost all GCNNs process a graph as though it is a ground-truth depiction of the relationship between nodes, but often the graphs employed in applications are themselves derived from noisy data or modelling assumptions. Spuri…
Graph convolutional neural networks (GCNN) have numerous applications in different graph based learning tasks. Although the techniques obtain impressive results, they often fall short in accounting for the uncertainty associated with the underlying graph structure. In the recently proposed Bayesian GCNN (BGCN) framework, this issue is tackled by viewing the observed graph as a sample from a parametric random graph model and targeting joint inference of the graph and the GCNN weights. In this paper, we introduce an alternative generative model for graphs based on copying nodes and incorporate i…
Beihang University（北京航空航天大学）；Beijing System Design Institute of Electro-Mechanic Engineering（北京机电工程总体设计所）；Peng Cheng Laboratory（鹏城实验室）
The Graph Convolutional Networks (GCN) proposed by Kipf and Welling is an effective model for semi-supervised learning, but faces the obstacle of over-smoothing, which will weaken the representation ability of GCN. Recently some works are proposed to tackle above limitation by randomly perturbing graph topology or feature matrix to generate data augmentations as input for training. However, these operations inevitably do damage to the integrity of information structures and have to sacrifice the smoothness of feature manifold. In this paper, we first introduce a novel graph entropy definition …
University of Amsterdam（阿姆斯特丹大学）；VU Amsterdam（阿姆斯特丹自由大学）；CIFAR（加拿大高等研究院）
Knowledge graphs enable a wide variety of applications, including question answering and information retrieval. Despite the great effort invested in their creation and maintenance, even the largest (e.g., Yago, DBPedia or Wikidata) remain incomplete. We introduce Relational Graph Convolutional Networks (R-GCNs) and apply them to two standard knowledge base completion tasks: Link prediction (recovery of missing facts, i.e. subject-predicate-object triples) and entity classification (recovery of missing entity attributes). R-GCNs are related to a recent class of neural networks operating on grap…
University of Amsterdam（阿姆斯特丹大学）；University of Edinburgh（爱丁堡大学）
Semantic role labeling (SRL) is the task of identifying the predicate-argument structure of a sentence. It is typically regarded as an important step in the standard NLP pipeline. As the semantic representations are closely related to syntactic ones, we exploit syntactic information in our model. We propose a version of graph convolutional networks (GCNs), a recent class of neural networks operating on graphs, suited to model syntactic dependency graphs. GCNs over syntactic dependency trees are used as sentence encoders, producing latent feature representations of words in a sentence. We obser…
In a business-to-business (B2B) customer relationship management (CRM) use case, each client is a potential business organization/company with a solid business strategy and focused and rational decisions. This paper introduces a graph-based analytics approach to improve CRM within a B2B environment. In our approach, in the first instance, we have designed a graph database using the Neo4j platform. Secondly, the graph database has been investigated by using data mining and exploratory analysis coupled with cypher graph query language. Specifically, we have applied the graph convolution network …
We present our ongoing work on understanding the limitations of graph convolutional networks (GCNs) as well as our work on generalizations of graph convolutions for representing more complex node attribute dependencies. Based on an analysis of GCNs with the help of the corresponding computation graphs, we propose a generalization of existing GCNs where the aggregation operations are (a) determined by structural properties of the local neighborhood graphs and (b) not restricted to weighted averages. We show that the proposed approach is strictly more expressive while requiring only a modest inc…
The distance-geometric graph representation adopts a unified scheme (distance) for representing the geometry of three-dimensional(3D) graphs. It is invariant to rotation and translation of the graph and it reflects pair-wise node interactions and their generally local nature. To facilitate the incorporation of geometry in deep learning on 3D graphs, we propose a message-passing graph convolutional network based on the distance-geometric graph representation: DG-GCN (distance-geometric graph convolution network). It utilizes continuous-filter convolutional layers, with filter-generating network…
Graph convolutional neural networks (GCNNs) have received much attention recently, owing to their capability in handling graph-structured data. Among the existing GCNNs, many methods can be viewed as instances of a neural message passing motif; features of nodes are passed around their neighbors, aggregated and transformed to produce better nodes' representations. Nevertheless, these methods seldom use node transition probabilities, a measure that has been found useful in exploring graphs. Furthermore, when the transition probabilities are used, their transition direction is often improperly c…
Ben-Gurion University（本-古里安大学）；University of British Columbia（不列颠哥伦比亚大学）
Graph Convolutional Networks (GCNs), similarly to Convolutional Neural Networks (CNNs), are typically based on two main operations - spatial and point-wise convolutions. In the context of GCNs, differently from CNNs, a pre-determined spatial operator based on the graph Laplacian is often chosen, allowing only the point-wise operations to be learnt. However, learning a meaningful spatial operator is critical for developing more expressive GCNs for improved performance. In this paper we propose pathGCN, a novel approach to learn the spatial operator from random paths on the graph. We analyze the…
TrafficKAN-GCN: Graph Convolutional-based Kolmogorov-Arnold Network for Traffic Flow Optimization
School of Mathematics and Applied Mathematics, University of Nottingham Ningbo China（诺丁汉大学宁波校区数学与应用数学学院）；School of Computer Science, University of Nottingham Ningbo China（诺丁汉大学宁波校区计算机科学学院）；Department of Electrical and Computer Engineering, University of Washington（华盛顿大学电气与计算机工程系）；School of Computer Science, Carnegie Mellon University（卡内基梅隆大学计算机科学学院）；School of Engineering, University of Nottingham Ningbo China（诺丁汉大学宁波校区工程学院）；School of Computer Science, University College Dublin（都柏林大学学院计算机科学学院）；The ADAPT SFI Research Centre（ADAPT SFI研究中心）
iRoC Technologies；Tallinn University of Technology（塔林理工大学）；Politecnico di Torino（都灵理工大学）
The paper is proposing a methodology for modeling a gate-level netlist using a Graph Convolutional Network (GCN). The model predicts the overall functional de-rating factors of sequential elements of a given circuit. In the preliminary phase of the work, the important goal is making a GCN which able to take a gate-level netlist as input information after transforming it into the Probabilistic Bayesian Graph in the form of Graph Modeling Language (GML). This part enables the GCN to learn the structural information of netlist in graph domains. In the second phase of the work, the modeled GCN tra…
